In this paper we prescribe a fourth order conformal invariant on the standard n-sphere, with n greater or equal to 5, and study the related fourth order elliptic equation. We first find some existence results in the perturbative case. After some blow up analysis we build a homotopy to pass from the perturbative case to the non-perturbative one under some flatness condition. Finally we state some existence results under the assumption of symmetry
Felli, V. (2002). Existence of conformal metrics on S^n with prescribed fourth order invariant. ADVANCES IN DIFFERENTIAL EQUATIONS, 7, 47-76.
Existence of conformal metrics on S^n with prescribed fourth order invariant
FELLI, VERONICA
2002
Abstract
In this paper we prescribe a fourth order conformal invariant on the standard n-sphere, with n greater or equal to 5, and study the related fourth order elliptic equation. We first find some existence results in the perturbative case. After some blow up analysis we build a homotopy to pass from the perturbative case to the non-perturbative one under some flatness condition. Finally we state some existence results under the assumption of symmetry
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